Tuesday, October 2, 2018

Raiders of the Lost Crucible

Filed under: Uncategorized — Tags: — m759 @ 11:22 AM

See other posts now tagged Crucible Raiders.

Related entertainment —

From YouTube:

From NBC:

For more from the above date,
Oct. 8, 2016, click "seriously" below.

But seriously

Sunday, September 30, 2018


Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

Click the above for an example.

Iconology of the Eightfold Cube

Filed under: Uncategorized — Tags: — m759 @ 11:13 AM

Found today in an Internet image search, from the website of
an anonymous amateur mathematics enthusiast

Forming Gray codes in the eightfold cube with the eight
I Ching  trigrams (bagua ) —

Forming Gray codes in the eightfold cube with the eight I Ching trigrams (bagua)

This  journal on Nov. 7, 2016

A different sort of cube, from the makers of the recent
Netflix miniseries "Maniac" —

See also Rubik in this  journal.

Saturday, October 31, 2015

Raiders of the Lost Crucible

Filed under: Uncategorized — Tags: — m759 @ 10:15 AM

Stanford Encyclopedia of Philosophy
on the date Friday, April 5, 2013 —

Paraconsistent Logic

"First published Tue Sep 24, 1996;
substantive revision Fri Apr 5, 2013"

This  journal on the date Friday, April 5, 2013 —

The object most closely resembling a "philosophers' stone"
that I know of is the eightfold cube .

For some related philosophical remarks that may appeal 
to a general Internet audience, see (for instance) a website
by I Ching  enthusiast Andreas Schöter that displays a labeled
eightfold cube in the form of a lattice diagram —

Related material by Schöter —

A 20-page PDF, "Boolean Algebra and the Yi Jing."
(First published in The Oracle: The Journal of Yijing Studies ,
Vol 2, No 7, Summer 1998, pp. 19–34.)

I differ with Schöter's emphasis on Boolean algebra.
The appropriate mathematics for I Ching  studies is,
I maintain, not Boolean algebra  but rather Galois geometry.

See last Saturday's post Two Views of Finite Space.
Unfortunately, that post is, unlike Schöter's work, not  
suitable for a general Internet audience.

Saturday, October 24, 2015

Two Views of Finite Space

Filed under: Uncategorized — Tags: , — m759 @ 10:00 AM

The following slides are from lectures on "Advanced Boolean Algebra" —

The small Boolean  spaces above correspond exactly to some small
Galois  spaces. These two names indicate approaches to the spaces
via Boolean algebra  and via Galois geometry .

A reading from Atiyah that seems relevant to this sort of algebra
and this sort of geometry —

" 'All you need to do is give me your soul:  give up geometry 
and you will have this marvellous machine.' (Nowadays you
can think of it as a computer!) "

Related material — The article "Diamond Theory" in the journal
Computer Graphics and Art , Vol. 2 No. 1, February 1977.  That
article, despite the word "computer" in the journal's title, was
much less about Boolean algebra  than about Galois geometry 

For later remarks on diamond theory, see finitegeometry.org/sc.

Saturday, February 22, 2014


Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

The title was suggested by a 1921 article
by Hermann Weyl and by a review* of
a more recent publication —

The above Harvard Gazette  piece on Davos is
from St. Ursula's Day, 2010. See also this  journal
on that date.

See as well a Log24 search for Davos.

A more interesting piece by Peter E. Gordon
(author of the above Davos book) is his review
of Charles Taylor's A Secular Age .
The review is titled

"The Place of the Sacred
in the Absence of God

(The place of the sacred is not, perhaps, Davos,
but a more abstract location.)

* Grundlagenkrise  was a tag for a Jan. 13, 2011,
  review in The New Republic  of Gordon's
  book on Cassirer and Heidegger at Davos.

Wednesday, January 22, 2014

A Riddle for Davos

Filed under: Uncategorized — Tags: , — m759 @ 9:00 PM

Hexagonale Unwesen

Einstein and Thomas Mann, Princeton, 1938

IMAGE- Redefining the cube's symmetry planes: 13 planes, not 9.

See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.

January 13 was also the dies natalis  of St. James Joyce.

Some related reflections —

"Praeterit figura huius mundi  " — I Corinthians 7:31 —

Conclusion of of "The Dead," by James Joyce—

The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live.

Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling.

A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.

Friday, April 5, 2013

The Crucible

Filed under: Uncategorized — Tags: — m759 @ 6:12 AM

"Though we had many pieces, we did not have the whole.
It was thirty years before we deciphered the formula.
But we did it at last.

There at night in the darkness of Fourier’s laboratory,
the four of us stood and watched the philosophers’ stone
forming in the crucible."

The Eight , by Katherine Neville
     (2008 Ballantine Books mass market edition, p. 640)

A journal post from August 25, 2009:

Image from a different journal earlier that same day, August 25, 2009:

Thirty-year medallion from Alcoholics Anonymous —


See also, in this  journal, "The Eight" + Damnation.

Thursday, December 27, 2012

Object Lesson

Filed under: Uncategorized — Tags: — m759 @ 3:17 AM

Yesterday's post on the current Museum of Modern Art exhibition
"Inventing Abstraction: 1910-1925" suggests a renewed look at
abstraction and a fundamental building block: the cube.

From a recent Harvard University Press philosophical treatise on symmetry—

The treatise corrects Nozick's error of not crediting Weyl's 1952 remarks
on objectivity and symmetry, but repeats Weyl's error of not crediting
Cassirer's extensive 1910 (and later) remarks on this subject.

For greater depth see Cassirer's 1910 passage on Vorstellung :

IMAGE- Ernst Cassirer on 'representation' or 'Vorstellung' in 'Substance and Function' as 'the riddle of knowledge'

This of course echoes Schopenhauer, as do discussions of "Will and Idea" in this journal.

For the relationship of all this to MoMA and abstraction, see Cube Space and Inside the White Cube.

"The sacramental nature of the space becomes clear…." — Brian O'Doherty

Saturday, September 24, 2011

Kernels of Being

Filed under: Uncategorized — Tags: — m759 @ 10:29 PM

For the Pope in Germany

"We wish to see Jesus. For somehow we know, we suspect, we intuit, that if we see Jesus we will see what Meister Eckhart might call “The Divine Kernel of Being”— that Divine Spark of God’s essence, God’s imago Dei, the image in which we are created. We seem to know that in seeing Jesus we just might find something essential about ourselves."

—The Reverend Kirk Alan Kubicek, St. Peter’s at Ellicott Mills, Maryland, weblog post of Saturday, March 28, 2009, on a sermon for Sunday, March 29, 2009

See also this journal in March 2009.

Related non-theology—

Weyl on coordinate systems, Cassirer on the kernel of being, and A Study in Art Education.

Wednesday, September 21, 2011

Symmetric Generation

Filed under: Uncategorized — Tags: , , — m759 @ 2:00 PM

Suggested by yesterday's Relativity Problem Revisited and by Cassirer on Objectivity

From Symmetric Generation of Groups , by R.T. Curtis (Cambridge U. Press, 2007)—

"… we are saying much more than that G M 24 is generated by
some set of seven involutions, which would be a very weak
requirement. We are asserting that M 24 is generated by a set
of seven involutions which possesses all the symmetries of L3(2)
acting on the points of the 7-point projective plane…."
Symmetric Generation , p. 41

"It turns out that this approach is particularly revealing and that
many simple groups, both sporadic and classical, have surprisingly
simple definitions of this type."
Symmetric Generation , p. 42

See also (click to enlarge)—


Cassirer's remarks connect the concept of objectivity  with that of object .

The above quotations perhaps indicate how the Mathieu group M 24 may be viewed as an object.

"This is the moment which I call epiphany. First we recognise that the object is one  integral thing, then we recognise that it is an organised composite structure, a thing  in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that  thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany."

— James Joyce, Stephen Hero

For a simpler object "which possesses all the symmetries of L3(2) acting on the points of the 7-point projective plane…." see The Eightfold Cube.

For symmetric generation of L3(2) on that cube, see A Simple Reflection Group of Order 168.

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